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Scale 591: "Gaptimic"

Scale 591: Gaptimic, Ian Ring Music Theory

Bracelet Diagram

The bracelet shows tones that are in this scale, starting from the top (12 o'clock), going clockwise in ascending semitones. The "i" icon marks imperfect tones that do not have a tone a fifth above. Dotted lines indicate axes of symmetry.

Tonnetz Diagram

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Tonnetz diagrams are popular in Neo-Riemannian theory. Notes are arranged in a lattice where perfect 5th intervals are from left to right, major third are northeast, and major 6th intervals are northwest. Other directions are inverse of their opposite. This diagram helps to visualize common triads (they're triangles) and circle-of-fifth relationships (horizontal lines).

Common Names

Zeitler
Gaptimic

Analysis

Cardinality6 (hexatonic)
Pitch Class Set{0,1,2,3,6,9}
Forte Number6-Z42
Rotational Symmetrynone
Reflection Axes1.5
Palindromicno
Chiralityno
Hemitonia3 (trihemitonic)
Cohemitonia2 (dicohemitonic)
Imperfections4
Modes5
Prime?yes
Deep Scaleno
Interval Vector324222
Interval Spectrump2m2n4s2d3t2
Distribution Spectra<1> = {1,3}
<2> = {2,4,6}
<3> = {3,5,7,9}
<4> = {6,8,10}
<5> = {9,11}
Spectra Variation3
Maximally Evenno
Maximal Area Setno
Interior Area2.25
Myhill Propertyno
Balancedno
Ridge Tones[3]
ProprietyImproper
Heliotonicno

Common Triads

These are the common triads (major, minor, augmented and diminished) that you can create from members of this scale.

* Pitches are shown with C as the root

Triad TypeTriad*Pitch ClassesDegreeEccentricityCloseness Centrality
Major TriadsD{2,6,9}231.5
Minor Triadsf♯m{6,9,1}231.5
Diminished Triads{0,3,6}231.5
d♯°{3,6,9}231.5
f♯°{6,9,0}231.5
{9,0,3}231.5
Parsimonious Voice Leading Between Common Triads of Scale 591. Created by Ian Ring ©2019 d#° d#° c°->d#° c°->a° D D D->d#° f#m f#m D->f#m f#° f#° f#°->f#m f#°->a°

Above is a graph showing opportunities for parsimonious voice leading between triads*. Each line connects two triads that have two common tones, while the third tone changes by one generic scale step.

Diameter3
Radius3
Self-Centeredyes

Modes

Modes are the rotational transformation of this scale. Scale 591 can be rotated to make 5 other scales. The 1st mode is itself.

2nd mode:
Scale 2343
Scale 2343: Tharimic, Ian Ring Music TheoryTharimic
3rd mode:
Scale 3219
Scale 3219: Ionaphimic, Ian Ring Music TheoryIonaphimic
4th mode:
Scale 3657
Scale 3657: Epynimic, Ian Ring Music TheoryEpynimic
5th mode:
Scale 969
Scale 969: Ionogimic, Ian Ring Music TheoryIonogimic
6th mode:
Scale 633
Scale 633: Kydimic, Ian Ring Music TheoryKydimic

Prime

This is the prime form of this scale.

Complement

The hexatonic modal family [591, 2343, 3219, 3657, 969, 633] (Forte: 6-Z42) is the complement of the hexatonic modal family [219, 1563, 1731, 2157, 2829, 2913] (Forte: 6-Z13)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 591 is 3657

Scale 3657Scale 3657: Epynimic, Ian Ring Music TheoryEpynimic

Transformations:

T0 591  T0I 3657
T1 1182  T1I 3219
T2 2364  T2I 2343
T3 633  T3I 591
T4 1266  T4I 1182
T5 2532  T5I 2364
T6 969  T6I 633
T7 1938  T7I 1266
T8 3876  T8I 2532
T9 3657  T9I 969
T10 3219  T10I 1938
T11 2343  T11I 3876

Nearby Scales:

These are other scales that are similar to this one, created by adding a tone, removing a tone, or moving one note up or down a semitone.

Scale 589Scale 589: Ionalitonic, Ian Ring Music TheoryIonalitonic
Scale 587Scale 587: Pathitonic, Ian Ring Music TheoryPathitonic
Scale 583Scale 583: Aeritonic, Ian Ring Music TheoryAeritonic
Scale 599Scale 599: Thyrimic, Ian Ring Music TheoryThyrimic
Scale 607Scale 607: Kadian, Ian Ring Music TheoryKadian
Scale 623Scale 623: Sycrian, Ian Ring Music TheorySycrian
Scale 527Scale 527, Ian Ring Music Theory
Scale 559Scale 559: Lylimic, Ian Ring Music TheoryLylimic
Scale 655Scale 655: Kataptimic, Ian Ring Music TheoryKataptimic
Scale 719Scale 719: Kanian, Ian Ring Music TheoryKanian
Scale 847Scale 847: Ganian, Ian Ring Music TheoryGanian
Scale 79Scale 79, Ian Ring Music Theory
Scale 335Scale 335: Zanimic, Ian Ring Music TheoryZanimic
Scale 1103Scale 1103: Lynimic, Ian Ring Music TheoryLynimic
Scale 1615Scale 1615: Sydian, Ian Ring Music TheorySydian
Scale 2639Scale 2639: Dothian, Ian Ring Music TheoryDothian

This scale analysis was created by Ian Ring, Canadian Composer of works for Piano, and total music theory nerd. The software used to generate this analysis is an open source project at GitHub. Scale notation generated by VexFlow, graph visualization by Graphviz, and MIDI playback by MIDI.js. Some scale names used on this and other pages are ©2005 William Zeitler (http://allthescales.org) used with permission.

Pitch spelling algorithm employed here is adapted from a method by Uzay Bora, Baris Tekin Tezel, and Alper Vahaplar. (An algorithm for spelling the pitches of any musical scale) Contact authors Patent owner: Dokuz Eylül University, Used with Permission. Contact TTO

Tons of background resources contributed to the production of this summary; for a list of these peruse this Bibliography.